R0 is assumed to be a constant so that the math / models work. But it really changes dramatically in practice. Maybe someone else will eventually make a model where the constant is more... constant. But until then, we will continue to use this model.
When I've looked into it, I've found it difficult to assess the degree to which we are looking at "behavior changes between seasons" vs "the season matters".
Reasons the season might matter: Thicker air (higher humidity) may reduce particulate spread. Viral lifespan may be different under different temperatures.
Yet, in researching the issue, I tend to find things like "well, in animal models, this is what we've seen". Or "we think the heat reduces the effectiveness of a protective membrane that the flu uses".
Despite some effort, I've not found sources that both (1) seem reliable, and (2) provide a clear/concise understanding of what we know and why/how we think we know these things.
They stuck a bunch of guinea pigs into a box, one box at 41F, a 2nd at 68F, and a third at 86F.
The box with 41F had the highest transmission rate. The box at 68F and 86F had lower transmission rates, even 0% transmission rate in the presence of 80% humidity.
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No such experiment exists for COVID19 yet. But because COVID19 continues to exponentially grow in the southern hemisphere (Australia in particular), there doesn't seem to be a relationship between temperature, humidity, and COVID19 like there is with the flu.
Edit: people down voting this, please look at definition and those papers. R_0 does changes.